Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x-5y &= 4 \\ 5x+3y &= -8\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $5x = -3y-8$ Divide both sides by $5$ to isolate $x$ $x = {-\dfrac{3}{5}y - \dfrac{8}{5}}$ Substitute this expression for $x$ in the first equation. $-3({-\dfrac{3}{5}y - \dfrac{8}{5}}) - 5y = 4$ $\dfrac{9}{5}y + \dfrac{24}{5} - 5y = 4$ Simplify by combining terms, then solve for $y$ $-\dfrac{16}{5}y + \dfrac{24}{5} = 4$ $-\dfrac{16}{5}y = -\dfrac{4}{5}$ $y = \dfrac{1}{4}$ Substitute $\dfrac{1}{4}$ for $y$ in the top equation. $-3x-5( \dfrac{1}{4}) = 4$ $-3x-\dfrac{5}{4} = 4$ $-3x = \dfrac{21}{4}$ $x = -\dfrac{7}{4}$ The solution is $\enspace x = -\dfrac{7}{4}, \enspace y = \dfrac{1}{4}$.